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    <title>rowinout</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>rowinout</b> -  inner-outer factorization</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Inn,X,Gbar]=rowinout(G)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>G</b>
        </tt>: linear system (<tt>
          <b>syslin</b>
        </tt> list) <tt>
          <b>[A,B,C,D]</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>Inn</b>
        </tt>:  inner factor (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>Gbar</b>
        </tt>:  outer factor (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>X</b>
        </tt>:  row-compressor of <tt>
          <b>G</b>
        </tt> (<tt>
          <b>syslin</b>
        </tt> list)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Inner-outer factorization (and row compression) of (<tt>
        <b>l</b>
      </tt>x<tt>
        <b>p</b>
      </tt>) <tt>
        <b>G =[A,B,C,D]</b>
      </tt> with <tt>
        <b>l&gt;=p</b>
      </tt>.</p>
    <p>
      <tt>
        <b>G</b>
      </tt> is assumed to be tall (<tt>
        <b>l&gt;=p</b>
      </tt>) without zero on the imaginary axis
    and with a <tt>
        <b>D</b>
      </tt> matrix which is full column rank.</p>
    <p>
      <tt>
        <b>G</b>
      </tt> must also be stable for having <tt>
        <b>Gbar</b>
      </tt> stable.</p>
    <p>
      <tt>
        <b>G</b>
      </tt> admits the following inner-outer factorization:</p>
    <pre>

         G = [ Inn ] | Gbar |
                     |  0   |
   
    </pre>
    <p>
    where <tt>
        <b>Inn</b>
      </tt> is square and inner (all pass and stable) and <tt>
        <b>Gbar</b>
      </tt> 
    square and outer i.e:
    Gbar is square bi-proper and bi-stable (Gbar inverse is also proper 
    and stable);</p>
    <p>
    Note that:</p>
    <pre>

         [ Gbar ]
   X*G = [  -   ]
         [  0   ]
   
    </pre>
    <p>
    is a row compression of <tt>
        <b>G</b>
      </tt> where <tt>
        <b>X</b>
      </tt> = <tt>
        <b>Inn</b>
      </tt> inverse is all-pass i.e:</p>
    <pre>

 T
X (-s) X(s) = Identity
   
    </pre>
    <p>
    (for the continous time case).</p>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../elementary/syslin.htm">
        <tt>
          <b>syslin</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="colinout.htm">
        <tt>
          <b>colinout</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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